Today I had to wait several hours in the lab for the freshman design seminar students to finish their designs, demo them, and turn in reports. Only the two LED cubes demoed their projects: the pulse monitor group had left their hardware in the lab last week by mistake, and it was gone; and the ultrasonic rangefinder group did not have the member with the software present—I’ll have to see if their report tells me how far they got.
Because I had to spend a lot of time in the lab today, I decided to redo the work mentioned in the post Ultrasonic transmitter impedance. That is, I tried measuring the (magnitude of) impedance of the transmitter at different frequency ranges, by measuring the voltage across the transmitter and across a series 2.2kΩ resistor at different frequencies. This time I had my laptop with me, and I plotted after every few measurements, so that I was careful to fill in frequencies whenever the impedance deviated from a simple capacitance.
The antiresonances around 42kHz and 56.5kHz are indicative of a coupled system—for the transmitter, the 39.78kHz, 42kHz, 55.4kHz, and 56.5kHz are probably different vibrational modes of the piezoelectric diaphragm.
One interesting observation was that the weird dip at 59.3kHz had hysteresis—if I approached it from below, I got the dip and it continued to about 59.4kHz, but if I approached it from higher frequencies, I could extend the capacitive line all the way back to 59.3kHz. I’ve no explanation for that yet.
I could probably do a better job of measuring at the extreme frequencies if my reference impedance were a 1nF or 2.2nF capacitor, since the voltage ratios would then be around 1 for most frequencies, and only being about a factor of 4 off at the resonances and antiresonances. The 50Ω output impedance of the function generator would not really be a problem until we got over a MHz, since the corner frequency would be 3.8MHz with a 1nF load. Of course, the capacitors I have are not very high precision, so I get more accurate measurements with resistors, even when the voltage ratios get fairly extreme.
I keep feeling that I should be able to use the magnitudes of the AC voltages to get the phase of the impedance (except for the sign), but all my attempts so far have resulted in mostly nonsense. At the resonances and anti-resonances the impedance appears to be purely real (that is, the voltages add up to about the same value as the for the low and high frequencies, where the transmitter is capacitive).